Question 148583
through (4,-2):



y=mx+b becomes
-2=m4+b


perpendicular to the line (3,7) and (5,6):
Find the slope of the goes that goes through (3,7) and (5,6) by putting the difference of the y's over the differences of the x's


7-6/3-5


Simplify that and get 

1/-2


Now flip it


-2/1


Now multiply it by -1


2/1


This is the slope you want for the equation.  Plug it in



y=mx+b becomes
-2=m4+b becomes
-2=2(4)+b


Now solve for b.  First simplify 2(4)


-2=8+b


Now subtract 8 from both sides


-10=b


Now set the equation up without the x and y coordinates:


y=mx+b becomes
y=2x-10----------------this is your answer in slope intercept form


To change it to standard form, move the x over to the other side.
y-2x=-10
or -2x+y=10


Slope-intercept: y=2x-10
Standard: -2x+y=10


Graph:
*[invoke describe_linear_equation -2, 1, -10]